# Vertical integration of gas exchange: from leaf light-response curves to crown light-use efficiency

The upscaling of leaf gas exchange to the entire tree crown will rely on the optimisation approach of Dewar (1996), based on the different sensitivity of assimilation and maintenance respiration to tissue nitrogen content. Whilst maintenance respiration can be assumed to be linearly related to total plant nitrogen content (Ryan 1991), photosynthesis will eventually saturate, so that maximum plant net primary production will be achieved at an intermediate level of nitrogen. It can be demonstrated that such an optimal balance implies a vertical profile of nitrogen content in the canopy, which closely matches the exponential profile of irradiance (see 3.6), in good agreement with experimental evidence. The linear relationship between nitrogen content and average daily irradiance (Equation 17) is explained in functional terms as:

${\displaystyle n_{l}^{opt}={\overline {I}}\cdot {\frac {\alpha }{{\overline {c_{i}}}\cdot k_{1}}}\cdot \left({\frac {1}{\lambda }}-1\right)}$ (27)

Figure 4: Percent of error in estimated <E> as a function of daily maximum VDP for uncorrected and corrected for a systematic linear component.

Daily plant net primary production can be then demonstrated to be linearly proportional to the amount of light intercepted by the crown over the entire day ${\displaystyle }$:

${\displaystyle =0.8\cdot \alpha \cdot \cdot \left(1-\lambda \right)^{2}}$ (28)

where the factor 0.8\textit{ }accounts for the biosynthetic efficiency of conversion of sugars to structural dry matter (Johnson 1990).

Experimental measurements on small seedlings grown under contrasting light regimes can provide an initial estimate for the parameter ${\displaystyle \lambda }$ in Equation 28, whose precise definition is however (Dewar 1996 and Appendix 1):

${\displaystyle \lambda ={\sqrt {\frac {r\cdot \left(1+\lambda _{sw}+\lambda _{r}\right)}{h\cdot {\overline {c_{i}}}\cdot k_{1}}}}}$ (29)

where r is tissue respiration per unit nitrogen content (assumed constant throughout the plant) and ${\displaystyle \lambda _{sw}}$ and ${\displaystyle \lambda _{r}}$ are the ratios of the nitrogen contents of live sapwood and fine roots, respectively, to the nitrogen content of the crown.

It follows from Equations 27-29 that tissue nitrogen content (and therefore leaf and plant assimilation) under conditions of full irradiance is not constant, but declines over the lifetime of the plant as the amount of nitrogen in the sapwood (and therefore its respiration load) increases. Figure 5 presents such a typical pattern in tree light-use efficiency, based on the assumption of a constant leaf-to-sapwood area ratio (hence a linear increase in sapwood biomass per unit foliage and respiratory costs with increasing height) and a constant foliage-to-fine root ratio.

This decline in leaf photosynthetic potential could easily explain the age-related decline in productivity commonly observed in mature trees (Ryan, Binkley, \& Fownes 1997), without any direct effects of age \textit{per se} (Landsberg et al. 1997).